If the cost. C, for manufacturing x units of a certain product is given by C= x² + 10x +30, find the number of units manufactured at a cost of $11,030.

  100 units

Step-by-step explanation:

We want to find x when ...

  C = 11030

  x² +10x +30 = 11030 . . . . fill in for C

  x² +10x = 11000 . . . . . . . . subtract 30

  x² +10x +25 = 11025 . . . . add 25 to complete the square

  (x +5)² = 105² . . . . . write as squares

  x +5 = ±105 . . . . . . . take the square root

  x = -5 ±105 = {-110, 100}

The number of units manufactured at a cost of $11,030 is 100.

The number of units manufactured at a cost of $11,030 was 100.

Step-by-step explanation:

I graphed the function on the graph below and found the point where C = 11,030. When C = 11,030, x is 100

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.